System and method to determine the prices and order quantities that maximize a retailer&#39;s total profit

ABSTRACT

The present invention provides a system and method for determining the prices and order quantities that maximize a retailer&#39;s expected profit by using a multi-dimensional distribution of the highest prices that customers are willing to pay. This is novel, as well in the literature as in the patent database. Brand switching is dealt with, taking into account that consumers who come into the store with a-priori preferences for products build a-posteriori preferences at the point of purchase based on actual retail prices and availabilities in the store.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present application generally relates to the pricing and ordering ofbrand-differentiated products in retailing (in the consumer durables andservices categories).

2. Background Description

While the problem is of great importance in practice, we are not awareof publications in the professional literature on systems and methodsfor establishing optimal prices and order quantities forbrand-differentiated products in retailing. A number of investigatorshave considered consumers' brand substitutability. See, for example, R.E. Bucklin and V. Srinivasan, 1991; A. Ching, T. Erdem, and M. Keane,2006; R. A. Colombo and D. G. Morrison, 1989; J. J. Inman and R. S.Winer, 1998; and A. Terech, R. E. Bucklin, and D. G. Morrison, 2003.

SUMMARY OF THE INVENTION

An embodiment of this invention relates to a method for determiningprices and order quantities that maximize a retailer's total profit.This method is based on consumer demand functions taking cross-priceelasticities into account. This kind of demand function is derived froma model that takes brand switching into account. We develop a new,simple approach to model customers' in-store brand choice as a functionof a distribution of maximum prices that they are willing to pay, whichcan be estimated based on a survey method. This novel approach to modelcustomers' brand choice is key for the application of the method, sincethe empirical estimation of consumer demand functions has been difficultdue to a lack of historical transaction or panel-type data for consumerdurables and services.

Brand-choice models in the professional literature mostly considerrepetitive shopping behavior, in particular purchases of perishablegoods in supermarkets, for which extensive data bases exist (Bucklin andSrivinasan, 1991; Inman and Winter, 1998; Ching et al., 2005). Whilesome of the brand models that could potentially be applied for consumerdurables classify consumers into hard-core loyals and potentialswitchers (Colombo and Morrison, 1989) or into groups with varyingdegrees of loyalty between these two extremes (Terech et al., 2003), ourmodel assumes that (1) everybody potentially switches brands and (2)that consumers decide depending on price and availability.

The present invention thus provides a system and method for determiningthe prices and order quantities that maximize a retailer's total profitby using a multi-dimensional distribution of the highest prices thatcustomers are willing to pay.

The present invention provides a model on optimal retail pricing andorder planning for horizontally differentiated products (brands) in agiven product category. To deduce customer demand functions undermulti-brand competition, it also models customer in-storebrand-switching behavior. Based on the deduced demand functions, thesystem and method solve the retailer's profit maximization problem forthe considered product category.

While one simplified version of the model presented herein considers twohorizontally differentiated products (brands), it can easily be extendedto several products. The products may be consumer durables or services.They could, for example, be consumer electronics or homeappliances—items that are bought occasionally and for which brandtypically matters. They could also be, for example, service contractsfor consumer electronics products and home appliances.

Usually, there is a lack of historical transaction or panel-type data onthe purchase of consumer durables, which makes the estimation ofconsumer demand functions difficult. This is why we present a simplemodel of in-store brand choice, which can be empirically estimated basedon a survey method. The principal assumption of this model is thatcustomers come into the store with a priori preferences for the productsbut then build a posteriori preferences at the point of purchase basedon the actual prices and availabilities in the store.

The model assumes a joint multi-dimensional distribution of customerpreferences rather than several one-dimensional distributions for eachof the brands. The model is kept very simple—e.g., it considers noconsumer factors such as age and income—for three major reasons:

-   -   First, the model is specifically designed for consumer durables,        which are purchased much less frequently than consumable        products such as groceries, with the result that huge data sets        are typically not available for consumer durables.    -   Second, the model takes into account the impact of limited        product availability on the customers' actual brand choice.    -   Third and foremost, the model deduces consumer demand functions        that are plugged into the retailer's profit maximization        function. The analysis is restricted to simple demand functions        in order to keep the retailer's profit maximization function        tractable.

The Basic Model

The basic model considers a retailer who is selling two products, X andY. The retailer buys products X and Y at given unit wholesale pricesw_(x) and w_(y), respectively. The wholesalers' list prices for productsX and Y are C_(x) and C_(y), respectively. The retailer's decisionvariables are the unit retail prices, P_(x) and P_(y), and thequantities x and y that he orders from the wholesalers of products X andY, respectively.

The basic model assumes that the retailer maximizes his expected profit,denoted as Π(.), from selling the two products. The expected profit is afunction of the quantities x and y, the retail prices P_(x) and P_(y)expected customer demand of product X, D_(x), and expected customerdemand of product Y, D_(y):

Π(x,y,P _(x) ,P _(y))=D _(x) P _(x) −xw _(x) +D _(y) P _(y) −yw_(y),  (1)

The treatment of expected demand is discussed below. The basic modelassumes that customers come to the store to buy either one unit ofproduct X or one unit of product Y or nothing. One may employ a brandswitching model tinder the assumption that customers come to theretailer's store with a priori preferences, represented by maximalprices they are willing to pay for either product (reservation prices).The upper boundary to these reservation prices is given by therespective list prices. Depending on the retail prices, P_(x) and P_(y),for X and Y, respectively, customers then build their a posterioripreferences so that they choose the product that yields the maximalsubjective gain, which is expressed by the difference of reservationprice and actual retail price. The model deduces expected customerdemand functions, D_(x) and D_(y), which depend on the distribution ofthe customers' joint a priori preferences for the two products, theretail prices and the retailer's capacities for products X and Y.

Consumer Demand Model

Customers' behavior may be modeled as follows: The probabilistic space{Ω,Prob} describes the set of customers. The number of customersvisiting a store is N. Each customer ωεΩ carries personal preferences,g_(x)(ω) and g_(y)(ω), toward product X and Y, respectively. Acustomer's preference for a product describes the maximal price thatthis customer is willing to pay for the product. Preferences are modeledby random variables with values between zero and the respective listprice. The upper boundary is due to the assumption that no individual iswilling to buy a product at a price above its list price. Note that thejoint multi-dimensional distribution of personal preferences builds thefoundation of the consumer demand model.

Case of Unlimited Supply

To begin with, the consumer demand model assumes that there is unlimitedsupply of products X and Y, so that every customer who decides to buy aproduct can get this product. Each customer ω decides to buy eitherproduct X or Y or neither of them in the following way. First heevaluates his subjective gain W_(x)(ω)=g_(x)(ω)−p_(x) for product X, andW_(y)(ω)=g_(y)(ω)−p_(y) for product Y. If both subjective gains, W_(x)and W_(y), are negative, the customer buys nothing. Otherwise, he buysthe product with the larger gain. If both gains are equal, we assumethat he buys product X. This is an arbitrary tie-breaking rule. It isunimportant, though, given the assumption of zero probability for suchan event to occur.

The expected demand function, D_(x), for product X is given by theprobability that W_(x) is positive and larger (or equal) than W_(y),multiplied by the number of customers N. Similarly, the expected demandfunction, D_(y), for product Y is given by the probability that W_(y) ispositive and larger than W_(x), multiplied by the number of customers N.

Case of Limited Supply

Customers, however, may face shortages in the supply of products Xand/or Y. Five different decisions are possible for each customer:

-   -   (1) If W_(x)(ω)<0 and W_(y)(ω)<0, customer ω buys nothing    -   (2) If W_(x)(ω)>W_(y)(ω)>0, customer ω buys product X if        available; otherwise he tries to buy product Y    -   (3) If W_(y)(ω)>W_(x)(ω)>0, customer ω buys product Y if        available; otherwise he tries to buy product X    -   (4) If W_(x)(ω)>0>W_(y)(ω), customer ω buys product X if        available, nothing otherwise    -   (5) If W_(y)(ω)>0>W_(x)(ω), customer ω buys product Y if        available, nothing otherwise

Define potential expected demands, U_(x) and U_(y), for products X andY, respectively, as the expected demand in the unlimited supply case.Hence, U_(x) is the expected number of customers making either decision(2) or (4). In other words, these are the customers with product X astheir first choice. Similarly, U_(y) is the expected number of customersmaking either decision (3) or (5). In other words, these are thecustomers with product Y as their first choice.

U _(x) =NProb{ω:decision(ω) is (2) or (4)}

U _(y) =NProb{ω:decision(ω) is (3) or (5)}  (2)

Define T_(x) as the expected number of customers making decision (2),(3), or (4). These are the customers who would consider buying product Xeven if not in the first place. Similarly, T_(y) is the expected numberof customers making decision (2), (3), or (5). These are the customerswho would consider buying product X even if not in the first place.

T _(x) =NProb{ω:decision(ω) is (2), (3), or (4)}

T _(y) =NProb{ω:decision(ω) is (2), (3), or (5)}  (3)

Remark 1: Potential expected demands depend on the actual retail prices,P_(x) and P_(y), because the prices influence the subjective gains andtherefore the probabilities of the particular decision.

In order to establish the actual expected demand functions, it isnecessary to consider what happens when one of the products is notavailable anymore. Our model represents consumer demand as the flow ofcustomers purchasing products over time and assumes that in such a flowthe customers' preferences are independent of the arrival moment.

Three cases are distinguishable, covering the various possiblesituations.

Case 1: If potential expected demands U_(x) and U_(y) are smaller thanorder quantities x and y, then the actual expected demands are identicalto the potential expected demands.

D_(x)=U_(x)

D_(y)=U_(y)

Case 2: Otherwise, suppose that the product X exhausts first. This meansthat x<U_(x), but it also means that x/U_(x)<y/U_(y). The portion ofcustomers who already visited the store is given by x/U_(x) at themoment when product X exhausts. The portion of customers who have notyet visited the store is 1−x/U_(x). The amount of product Y sold up tothis moment is equal to U_(y) x/U_(x). In this case, the expected demandfor product X is equal to order quantity x. The expected demand forproduct Y is the minimum of the order quantity y and the sum of thedemand up to the exhaustion moment, U_(y) x/U_(x), and the expecteddemand after this moment, (1−x/U_(x)) multiplied by T_(y), the number ofcustomers who would consider buying product Y even if not in the firstplace.

D_(x)=x

D _(y)=min[y,U _(y) x/U _(x)+(1−x/U _(x))T _(y)]

Case 3: Similarly, if the product Y exhausts first, y<U_(y) andy/U_(y)<x/U_(x):

D _(x)=min[x,U _(x) y/U _(y)+(1−y/U _(y))T _(x)]

D_(y)=y

Demand for all three cases may be written in a more compact way.

D _(x)=min[x,U _(x) y/U _(y)+(1−y/U _(y))⁺ NProb{ω:decision(ω) is (4)}]

D _(y)=min[y,U _(y) x/U _(x)+(1−x/U _(x))+NProb{ω:decision(ω) is(5)}]  (4)

where the + sign in the superscript means that we take the value of theexpression if it is positive and zero otherwise.

Retailer's Profit Maximization

The retailer's expected profit maximization (equation (1)) yieldsoptimal retail prices P_(x)* and P_(y)* and optimal order quantities x*and y*.

Properties of the Model with Two Products

We cannot present a closed-form solution to the retailer's expectedprofit maximization problem because of its complexity. Thus, in general,the solution has to be found numerically. Nonetheless, the closed-formsolution for a specific customer preference distribution is discussed inthe example below.

In general, we are able to identify a number of properties of theretailer's profit function. We formulate them for product X but theyhold analogously for product Y.

Property 1: The expected potential demand U_(x) as a function of theretail prices, P_(x) and P_(y), is non-increasing in P_(x) andnon-decreasing in P_(y). These are the customers whose first choicewould be X, given the prices P_(x) and P_(y).

Property 2: The expected number of customers who would consider buyingproduct X even if not in the first place is non-increasing in P_(x) andindependent of P_(y).

Property 3: If the retailer is not obliged to order positive quantities,then his optimal expected profit is non-negative. This implies that theoptimal solution might require zero order quantities in some situations.These situations may be caused by the wholesale price exceeding thepreferences of all customers. They may also be caused by a much lowerprofit margin for one product than for the other product, so that theretailer's interest is to drive as many customers as possible to themore profitable product.

Property 4: There always exists an optimal solution with retail pricesnot below the wholesale prices.

Property 5: For any retail prices, P_(x) and P_(y), and any orderquantity x, ordering more than U_(y)x/U_(x)+(1−x/U_(x))⁺N Prob{ω:decision(ω) is (5)} yields a lower expected profit than ordering exactlythis amount:

Π(x,y,P _(x) ,P _(y))≦Π(x,D _(y) ,P _(x) ,P _(y))  (5)

Property 6: For prices and order quantities maximizing the retailer'sexpected profit, we have

D _(y)(x*,y*,P _(x) *,P _(y)*)=y*  (6)

In other words, the expected demand for product Y is equal to the orderquantity of product Y if the prices and order quantities are optimal.

Property 7: Ordering both products, X and Y, above expected potentialdemands yields lower expected profit than ordering exactly expectedpotential demands of both products.

If

P_(x)>w_(x), and P_(y)>w_(y), and x≧U_(x), and y≧U_(y),  (7)

then

Π(x,y,P _(x) ,P _(y))≦Π(U _(x) ,U _(y) ,P _(x) ,P _(y))

Property 8: There are cases where the order quantity for one of the twoproducts larger than the expected potential demand for this productyields a higher expected profit than ordering the expected potentialdemand. In this case, the order quantity for the other product is zero.

Assume that

P_(x)>w_(x), and P_(y)>w_(y), and x<U_(x).

If

U _(x)(P _(x) −w _(x))<NProb{ω:decision(ω) is (2)}(P _(y) −w _(y)),  (8)

then

Π(x,y,P _(x) ,P _(y))≦Π(0,T _(y) ,P _(x) ,P _(y)),

otherwise

Π(x,y,P _(x) ,P _(y))≦Π(U _(x) ,U _(y) ,P _(x) ,P _(y)).

Property 9: For given retail prices, the optimal order quantity of aproduct is equal either to zero (and then the product is not offered atall) or to the expected number of customers for whom this product is thefirst choice.

Extension of the Model to More Than Two Products

When more than two products are available the search for the optimalsolutions (largest retailer's profit) may be very complicated due to thehighly non-linear dependence of the profit from the proposed retailprices. In addition, the domain of the definition of the profit functionis partitioned into regions (of the different quantities) where it hasdifferent forms. Moreover, it is important to consider thebrand-switching phenomenon at the moment when the supply does not meetthe demand. Fortunately, only a finite set of possible procurementquantities comes into consideration. Namely, for each group of proposedretail prices, and therefore for each distribution of subjective gains,it is enough to check the collection of subset of products the retailerwishes to order from the wholesaler. For each such subset, the optimalquantities for any product are determined by the number of customerswhose first preference is this product (assuming it will be provided).Thus, the optimum to be calculated is not an optimum over all retailprices and all quantities but is instead an optimum over all retailprices and all the (finite) subsets of products to be procured from thewholesaler.

An Example with Closed-Form Solution

This example assumes that the distribution of preferences is perfectlynegatively correlated, so that, for each customer ω,

g _(x)(ω)/C _(x) +g _(y)(ω)/C _(y)=1.

This means that the pair of preferences (g_(x), g_(y)) lies for eachcustomer on the segment of the straight line between the points(C_(x),0) and (0,C_(y)). Moreover, it is assumed that on this segmentthe distribution is uniform.

This allows one to calculate the probabilities of the customers'decisions (1) through (5), which will uniquely depend on the retailprices:

Deci- sion Buy Probability (1) Nothing Max{0, P_(x)/C_(x) + P_(y)/C_(y)− 1} (2) X, otherwise Y Max{C_(x)/(C_(x) + C_(y))(1 − P_(x)/C_(x) −P_(y)/C_(y)), 0} (3) Y, otherwise X Max{C_(y)/(C_(x) + C_(y))(1 −P_(x)/C_(x) − P_(y)/C_(y)), 0} (4) X, otherwise nothing Min{P_(y)/C_(y),1 − P_(x)/C_(x)} (5) Y, otherwise nothing Min{P_(x)/C_(x), 1 −P_(y)/C_(y)}

The first choices in the Max and Min expressions correspond to the casethat P_(x)/C_(x)+P_(y)/C_(y)<1, while the second choices correspond tothe case that P_(x)/C_(x)+P_(y)/C_(y)>1.

Plugging these probabilities into the retailer's profit function andusing the properties discussed above, one finds the optimal profit

Π(x*,y*,P _(x) *,P _(y)*)=N/4[(C _(x) −w _(x))² /C _(x)+[(C _(y) −w_(y))² /C _(y)]  (9)

at

x*=N(1−P _(x) /C _(x))

y*=N(1−P _(y) /C _(y))

P _(x)*=(C _(x) +w _(x))/2

P _(y)*=(C _(y) +w _(y))/2

An Application to More General Distributions

As stated above, it is in general not possible to find a closed-formsolution and recourse must be made to numerical methods.

Suppose that the distribution of customer preferences is given in formof a table. In the case of two brands, it is a two-dimensional table.The rows and columns of this table represent the intervals of thepreferences of the two products. The entries of the table represent thenumber of customers with preferences in those intervals.

Assume a pair of wholesale prices. For each pair of retail prices aboveor equal to the respective wholesale prices, one can calculate thenumber of customers making a decision (1) through (5), makinginterpolations if necessary (assuming uniform distribution in eachcell). Using the formulas for demand and the properties discussed above,one may calculate the optimal quantities for each pair of retail pricesand the corresponding retailer's profit, thus making it possible tochoose the optimal pair of retail prices.

The present invention thus provides a system, a method, and amachine-readable medium for providing instructions for a computer, which

-   -   given a distribution of upper limits of prices a consumer is        willing to pay for each of a plurality of products given their        list prices, and    -   given wholesale price data for a plurality of products,        determines profit-maximizing retail prices and amounts of        products to be ordered and provides the resulting list of        quantities and prices as one or more of a printout, a        machine-readable data output to storage, and directly as inputs        to data processing. The computer may be connected to a network,        and the network may be the Internet. Said wholesale price data        and the distribution of customer preferences may be obtained        from a database connected to such a network.

The method, system, and machine-readable medium thus provided accordingto the present invention determine prices and order quantities thatmaximize a retailer's expected profit for a specific product categoryby: using a computer to determine expected demand for products based ona distribution of upper limits of prices each customer is willing to payfor each of a plurality of products and based on given proposed retailprices; using a computer to determine an amount of products to beordered by calculating profit based on one or more of availablewholesale price data, proposed retail prices, and said determined demandat said proposed retail prices; using a computer to determine retailprices based on available wholesale prices, a distribution of upperlimits of prices each customer is willing to pay for given products, andsaid determined demand for products and said determined orderquantities, both depending on retail prices; and providing a list ofquantities and prices as one or more of a printout, a machine-readabledata output to storage, and directly as input to data processing. Thecomputer may or may not be connected to a network, and the network mayor may not be the Internet. The wholesale price data may or may not beobtained from a database connected to such a network. The retail pricesdetermined by the computer may or may not be profit-maximizing retailprices.

The present invention provides a computer-implemented method fordetermining prices and order quantities that maximize a retailer'sexpected profit for a specific product category comprising the steps of:using a customer survey to determine prices customers are willing to payfor a product; and based on said survey, using a computer to define amodel of customers' in-store brand choice as a function of adistribution of prices customers are willing to pay. The pricesdetermined by this method may or may not be maximum prices customers arewilling to pay.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a schematic for maximization of retailer's expected profit(simply denoted as profit hereafter) given wholesale prices andcustomers' preferences.

FIG. 2 shows a schematic for determination of optimal quantities whenretail and wholesale prices are known.

FIG. 3 shows a schematic for determination of the distribution ofcustomer preferences depending of retail prices.

FIG. 4 shows an example of a system according the claimed invention, inwhich wholesale price data is obtained over a network.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS OF THE INVENTION

The present invention produces the prices and order quantities thatmaximize a retailer's total profit for a specific product category,taking the distribution of customer preferences into account, under thefollowing given conditions:

-   -   There is a joint multi-dimensional distribution of the highest        prices customers are willing to pay, estimated based on survey        or historical data (described, for example, as a multi-index        table or a database), the number of indices in such a table        would correspond to the number of brands while the dimension of        each index would correspond to the number of considered        price-intervals for the respective brand. The entries of such a        table would be the percentage of customers for whom the        respective prices are the maximally acceptable prices for each        of the brands.    -   There is a known monetary cost of each brand to the retailer,        including the unit wholesale price, shipping, storage, shelf and        others.    -   There is a the list price of each of the brands, representing        caps to the multi-index preference table.    -   There is a given estimated total number of customers visiting        the store.        Taking those conditions as given, the procedure of the present        invention is as follows.    -   A. For any proposed list of retail prices, using the        distribution of highest prices customers are willing to pay,        determine the distribution of subjective gains. Each customer        orders the products he is willing to buy by the highest,        nonnegative subjective gain, assuming that it is available.    -   B. Using the distribution of customers with the same ordering        for the proposed retail prices and for each subset of available        products, determine the demands for each product. This will        constitute the amounts of each product to be ordered.    -   C. Using the calculated amounts to be ordered, given wholesale        prices and proposed retail prices, calculate the profit of the        retailer.    -   D. Maximize the profit by choosing the list of retail prices        that yields the highest profit. The result of this procedure is        a list of order quantities and prices, which may be provided as        a graphic or nongraphic printout, and/or as machine-readable        data output to storage or directly as input to data processing,        for use in ordering and pricing application.

Referring now to the drawings, and more particularly to FIG. 1, whichshows the complete process, there is shown the maximization ofretailer's profit given wholesale prices and customers' preferences.Starting with proposed retailer prices for all products, as shown instep 210, the proposed retail prices are used as input, as shown in step211, to establish the distribution of customers' subjective gains, asshown in step 430. Also used as input for step 430 is the knowledge ofthe distribution of the highest prices each customer is willing to payfor each of the products, as shown in step 410. Both the distribution ofcustomers' subjective gains, as shown in step 430, and the knowledge ofwholesale prices, as shown in step 229, are used to calculate quantitiesthat maximize a retailer's profit, as shown in step 227. Profit is thencalculated based on proposed retail prices and calculated demands andquantities, as shown in step 131. In step 135, a determination is madewhether all retail prices have been checked. If no, then a newproposition of retail prices is chosen as shown in step 137, with thenew proposition being used to update the proposed retail prices for allproducts in step 211. Steps are reiterated, beginning with step 430,using the updated step 211 as input. When step 135 determines that allretail prices have been checked, the retail prices and implicitquantities that maximize the retailer's profit are found, as shown instep 140, and the process is ended, as shown in step 250.

FIG. 2 details step 227, showing the determination of optimal quantitiesto order when retail and wholesale prices are known. Beginning withknowledge of the distribution of customers' highest prices, as shown instep 410, and proposed retail prices for all products, as shown in step211, the distribution of customers' subjective gains is established, asshown in step 430. A Subset of products is then chosen, as shown in step313, and, for each product in this subset, the number of customers withthe highest preference for that product is estimated, as shown in step315. Taking the number of customers with the highest preference for aproduct as the quantity to be ordered, as shown in step 321, theretailer's profit is calculated, as shown in step 331, based onknowledge of wholesale prices, as shown in step 229, as well as onproposed retail prices, the above established quantities, and the givensubset of products. In step 335, a determination is made whether allsubsets have been checked. If no, then a new subset is chosen as shownin step 337, with the new subset being used to update the choice ofsubset of products in step 313. Steps are reiterated, beginning withstep 315, for the updated choice of step 313. When step 335 determinesthat all subsets have been checked, the subset and implicit quantitieswhich maximize the retailer's profit for given prices are found, asshown in step 227 in FIG. 1.

Referring to FIG. 3, which details step 430, there is shown thedetermination of the distribution of customer preferences depending onproposed retail prices. This figure shows in greater detail howknowledge of customers' highest prices and the retail prices for all, asshown in steps 410 and 211 of FIG. 2, is used as input to establish thedistribution of customers' subjective gains, as shown in step 430 ofFIG. 2. An investigation of the distribution of the highest prices eachcustomer is willing to pay is undertaken, as shown in step 110,resulting in knowledge of the distribution of the highest prices eachcustomer is willing to pay, as shown in step 410. That knowledge is usedas input for step 423, in which each customer compares the retail pricesof each product with the price the customer is willing to pay. Also usedas input for step 423 is the retail price for each product, as shown instep 121. Based on the customer comparison of step 423, the comparisonproduces a determination of subjective gains a customer expects from aproduct, as shown in step 424. For each product, if the subjective gaindoes not pass some threshold, then the product will not be purchased, asshown in step 425; by contrast, all the products that do pass thethreshold are ordered according to the size of the subjective gain, asshown in step 426. All the customers are then grouped by the order inwhich they prefer the products, as shown in step 430. The result, asshown in step 430, is to establish a distribution of the groups ofcustomers with the same ordered preferences.

FIG. 4 shows an example of a system according the claimed invention, inwhich wholesale price data is obtained over a network. A computer 500has a machine-readable medium 510 for providing instructions. Anoperator 540 is able to provide input via a keyboard 521 or mouse 525,and the computer is able to provide output via a monitor 531 or aprinter 535. The computer is connected to a network 550 to which isconnected a database 560 from which the computer may obtain wholesaleprice data. Other data may be obtained from other databases 570 a, 570b, and 570 c connected to the network 550.

The manager 540 of a retail store who wants to determine orderquantities and retail prices of a number of products in a specificcategory may thus use the computer 500, which runs software based on thepresent invention. The program pulls information on customer preferencesfrom a remote data base 570 a, and the manager enters information onwholesale prices using the keyboard 521 or copies it from a portablememory device 510. This is one example; data input may be provided inmany different ways. The manager 540 then employs thecomputer-implemented method of the present invention to determineprofit-maximizes prices and order quantities. The resulting list ofoptimal retail prices and optimal quantities to order is displayed onthe screen 531, printed out on printer 535 and stored in a database 560.The data stored in database 560 can be streamlined into other software.

While the invention has been described in terms of a single preferredembodiment, those skilled in the art will recognize that the inventioncan be practiced with modification within the spirit and scope of theappended claims.

1-5. (canceled)
 6. A system for determining prices and order quantitiesthat maximize a retailer's total profit for a specific product categorycomprising: a computer to determine demand for products based on adistribution of upper limits of prices each customer is willing to payfor each of a plurality of products and based on given proposed retailprices; a computer to determine an amount of products to be ordered bycalculating profit based on one or more of available wholesale pricedata, proposed retail prices, and said determined demand at saidproposed retail prices; a computer to determine retail prices based onavailable wholesale prices, a distribution of upper limits of priceseach customer is willing to pay for each of a plurality of products, andsaid determined demand for given products and said determined orderquantities, both depending on retail prices; and a computer to providethe resulting list of quantities and prices as one or more of aprintout, a machine-readable data output to storage, and directly asinput to data processing.
 7. The system of claim 6, wherein the computeris connected to a network.
 8. The system of claim 7, wherein the networkis the Internet.
 9. The system of claim 7, wherein said wholesale pricedata is obtained from a database connected to said network.
 10. Thesystem of claim 6, wherein said computer-determined retail prices areprofit-maximizing retail prices.
 11. A machine-readable medium fordetermining prices and order quantities that maximize a retailer's totalprofit for a specific product category by: instructing a computer todetermine demand for products based on a distribution of upper limits ofprices each customer is willing to pay for each of a plurality ofproducts and based on given proposed retail prices; instructing acomputer to determine an amount of each of products to be ordered bycalculating profit based on one or more of available wholesale pricedata, proposed retail prices, and said determined demand at saidproposed retail prices; instructing a computer to determine retailprices based on available wholesale prices, a distribution of upperlimits of prices each customer is willing to pay for each of givenproducts, and said determined demand for products and said determinedorder quantities, both depending on retail prices; and instructing acomputer to provide the resulting list of quantities and prices as oneor more of a printout, a machine-readable data output to storage, anddirectly as input to data processing.
 12. The machine-readable medium ofclaim 11, wherein the computer being instructed is connected to anetwork.
 13. The machine-readable medium of claim 12, wherein thenetwork is the Internet.
 14. The machine-readable medium of claim 12,wherein said wholesale price data is obtained from a database connectedto said network.
 15. The machine-readable medium of claim 11, whereinsaid computer-determined retail prices are profit-maximizing retailprices.
 16. A method for determining prices and order quantities thatmaximize a retailer's expected profit for a specific product categorycomprising the steps of: using a customer survey to determine pricescustomers are willing to pay for a product; and based on said survey,defining a model of customers' in-store brand choice as a function of adistribution of prices customers are willing to pay.
 17. The method ofclaim 16, wherein said prices are maximum prices customers are willingto pay.